I think it would be great if climbers were required to do a bit of community service and pick up trash to be bagged. Then, send up balloons to let the wind carry the trash away from the mountain. If coordinated, drones could catch the floating trash bags for proper disposal. Teams could gradually get rid of the bodies, too.
Make it part of the acclimatization process as the climbers do that cycle of going part way up the mountain and then returning to a lower camp. A climber is only allowed to try for the summit after doing their community service.
The problem is that neither Nepal nor Tibet have any desire to limit the lucrative climbing permits that are issued for Everest. Anything that stands in the way of collecting fees will be opposed.
Teams could gradually get rid of the bodies, too.
As a side note, each guide group should be required to salvage the body of anyone who dies and bring them back to the base instead of just leaving them behind.